Luis Zambrano-Cruzatty, Ph.D.

Spring 2025

Recap

We learned how to plot and read GSD curves.
We learned how to determine the soil fractions.
We learned how to calculate particle sizes and gradation coefficients.

Atterberg limits
USCS classification
AASHTO classification

Objectives covered in this lecture

[O1]: Develop an understanding of soil phase relations, index properties, and their application to soil classification and compaction

After this lecture we will able to:

Calculate Atterberg limits and the activity of soils.
Classify soils according to the USCS and AASHTO.

Consistency limits

Also known as Atterberg limits after soil scientist who proposed them (Albert Atterberg). The Atterberg limits are thresholds of water content at which the behavior of soils changes.

There are three important limits:

The liquid limit.
The plastic limit.
The shrinkage limit.

Note:

You will perform tests to determine this limits in your laboratory practice. You will have fun!

Liquid limit (ASTM D4318)

$LL$: Is the water content at which a standard groove cut in the soil will close 0.5" at 25 blows.

Arthur Casagrande refined the method to measure $LL$ using the Casagrande cup method.
You will learn the steps of the test in your laboratory class.
Plot $w$ vs. $N_{blows}$. The $N$ axis must be in logarithmic scale.
Interpolate $LL$ from curve.

Note: Most soils will have $LL$ less than 100%. However, it can be as high as 300%.

Example 2.9

A liquid limit test was conducted on a soil and resulted in the data shown below. Find the liquid limit.

Test No	Wet soil + container	Dry soil + container	Container	N
1	17.71	15.27	5.23	32
2	20.08	16.78	5.21	30
3	24.31	19.25	5.1	28
4	16.45	13.2	5.11	26
5	18.35	14.23	5.13	23
6	26.80	19.45	5.11	21

Plastic limit (ASTM D4318)

$PL$: Is the water content at which soil crumbles when rolled to a diameter of 3 mm.

Determined by rolling clay snakes
Results are operator dependent.
Repeat at least three times.
$PL$ is the average water content of the total number of tests performed.

Note: Most soils have $PL < 40$%.

Example 2.10

The results of a plastic limit test are shown in the table below. Calculate the plastic limit.

Test No	Wet soil + container	Dry soil + container	Container
1	17.34	16.2	5.11
2	18.07	16.79	5.13
3	15.20	14.25	5.14
4	16.66	15.46	5.11

Shrinkage limit (ASTM D4943)

$SL$: Is the water content at which volume change stops when the soil is further desiccated.

$ SL=\left(\frac{V_{dry} \gamma_w}{W_s}-\frac{1}{G_s}\right) \times 100$

Procedure to calculate $SL$

Pour wet soil in container of known volume and weigh it.
Put the sample in the oven until it is fully dry. This will shrink the sample.
Measure change of volume using mercury.

Other methods exist to meassure the volume of the dry pat. One of such involves the use of wax.

Example 2.11

During the determination of the shrinkage limit of a sandy clay, the following laboratory data was obtained:

Wet wt. of soil + dish= 87.85 g
Dry wt. + dish= 76.91 g
Wt. dish = 52.7 g

Volumetric determination of soil pat:

Wt. of dish + mercury= 430.8 g
Wt. of dish = 244.62 g

calculate the $SL$ assuming $G_s=2.65$.

Consistency indices

$PI$: Is the range of water content in which the fine fraction of soils behaves as a plastic material.

$$ PI=LL-PL $$

$LI$: is a scaling parameter that maps the natural water content to the consistency limits.

$$ LI=\cfrac{w_n-PL}{PI} $$

Quiz 2.11

What is the value of the liquidity index $LI$ when $w_n=PL$?

0
-1
2
0.5
inf.

Quiz 2.12

What is the value of the liquidity index $LI$ when $w_n=LL$?

0
-1
2
0.5
1

Activity of clays

$A$: Is the ratio of the plasticity index $PI$ to the clay fraction $C_F$.

$ A=PI/CF$

$A$ is highly correlated to clay mineralogy.
$0.75 \leq A \leq 1.25 \implies$ "Normal soils''
$A < 0.75 \implies$ "inactive"
$A>1.25 \implies $ "active"

Mineral	Activity
Na-montmorillonite	4-7
Ca-montmorillonite	1.5
Illite	0.5-1.3
Kaolinite	0.3-0.5
Hallosyte (dehydrated)	0.5
Hallosyte (hydrated)	0.1
Attapulgite	0.5-1.2
Allophane	0.5-1.2
Mica (muscovite)	0.2
Calcite	0.2
Quartz	0

Quiz 2.13

How can we obtain the clay fraction $C_F$ of a soil?

Sieve analysis
Casagrande cup
Plastic limit test
Hydrometer analysis
All of the above

Example 2.12

For the parameters shown in the table, compute $LL$, $PI$, $LI$, and $A$

Soil classification

Geotechnical Engineers classify soils using the Unified Soil Classification System (USCS) for consistent naming.

Group symbols

Two letters
- First letter $\longrightarrow$ dominant fraction.
- Second letter $\longrightarrow$ minor fraction
Dominant fraction
- Coarse (retained in sieve No 200).
  - Gravel (G), sand (S).
- Fines (passing sieve No 200).
  - Silt (M), clay (C), organic content (O).
Minor fraciton
- Coarse, depending on well/poorly-graded (W, P) and fines (M, C).
- Fine, depending on low/high plasticity (L,H).

Plasticity chart

USCS flow diagram for fines $F_F \geq 50\%$

USCS flow diagram for $F_F < 50\%$

Example 2.13

Classify the soil with data shown in the GSD below.

Is $F_F \geq 50\%$?
No $\implies$ Either S or G
Is $S_F > G_F$?
Yes $\implies$ first letter is S
What is $F_F$?
$F_F < 5\%$
What is $C_u$?
$C_u<6 \ \text{and/or} \ [C_c<3 \cup C_c>3] $ is true $\implies$ second letter is P
Is $G_F< 15\%$?
Yes $\implies$ soil is SP Poorly graded sand

Example 2.15

Classify the soil with data shown in the GSD below. Go to Jupyter Notebook

Example 2.16